Tag: reverse causality

What is the impact of the slave trades on economic progress in Africa? Are the modern African states which ‘exported’ a higher number of slaves more likely to be underdeveloped several centuries afterwards?

Harvard economist Nathan Nunn addresses these questions in his chapter for the “Natural experiments of history” collection. The edited volume is supposed to showcase a number of innovative methods for doing empirical research to a broader audience, and historians in particular. But what Nunn’s study actually illustrates is the difficulty of making causal inferences based on observational data. He claims that slave exports contributed to economic underdevelopment, partly through impeding ethnic consolidation. But his data is entirely consistent with a very different interpretation: ethnic diversity in a region led to a higher volume of slave exports and is contributing to economic underdevelopment today. If this interpretation is correct, it could render the correlation between slave exports and the lack of economic progress in different African states spurious – a possibility that is not addressed in the chapter.

The major argument of Nunn’s piece is summarized in the following scatterplot. Modern African states from which more slaves were captured and exported (correcting for the size of the country) between the XVth and the XIXth centuries are associated with lower incomes per capita in 2000 (see Figure 5.1 on p.162, the plot reproduced below is actually from an article in the Quarterly Journal of Economics which looks essentially the same):

The link grows only stronger after we take into account potential ‘omitted variables’ like geographical location, natural openness, climate, natural resources, history of colonial rule, religion and the legal system. Hence, the relationship seems more than a correlation and Nunn boldly endorses a causal interpretation: “the slave trades are partly responsible for Africa’s current underdevelopment” (p.165).

Not being a specialist in the history of slavery, my initial reaction was one of disbelief – the relationship seems almost too good to be true. Especially when we consider the rather noisy slave exports data which attributes imperfect estimates of slave exports to modern states which didn’t exist at the time when the slaves were captured and traded. While it is entirely plausible that slave exports and economic underdevelopment are related, such a strong association several centuries apart between the purported cause and its effect invites skepticism.

It seemed perfectly possible to me that the ethnic heterogeneity of a territory can account for both the volume of slave exports, and current economic underdevelopment. In my layman’s worldview, people are more likely to hunt and enslave people from another tribe or ethnicity than their own. At the same time, African countries in which different ethnicities coexist might face greater difficulties in providing public goods and establishing the political institutions conductive to economic prosperity. So I was a bit surprised that the analysis doesn’t control for ethnic diversity, in addition to size, climate, openness, etc.

But then towards the end of the essay, the relationship between slave exports and ethnic diversity is actually presented and the correlation at the country level turns out to be very high. But Nunn decides to interpret the relationship in the opposite direction: for him, slave exports caused ethnic diversity by impeding ethnic consolidation (which in turn contributes to economic underdevelopment today). He doesn’t even consider the possibility of reverse causality in this case, although the volume of slave exports could easily be a consequence rather than a cause of ethnic diversity in a region.

Of course, data alone cannot give an answer which interpretation is more likely to be correct. And this is exactly the point. When the assignment of countries into different levels of slave exports is not controlled by the researcher or randomized by nature, it is imperative that all possible interpretations consistent with the data are discussed and evaluated; especially in a volume which aims to bring research methodology lessons to the masses.

And finally, if my suggestion that ethnic diversity is more likely to be a cause rather than an effect of slave exports is correct, can ethnic diversity explain away the correlation between slave exports and economic performance? While Nunn doesn’t test this conjecture, he has the data available on his website, so why don’t we go ahead and check: while I can’t be entirely sure I replicate exactly what the original article is doing [there is no do-file online], a regression of income on slave exports with ethnic diversity included as a covariate takes the bulk of the significance of slave exports away.

Is unit homogeneity a sufficient condition (assumption) for causal inference from observational data?

Re-reading King, Keohane and Verba’s bible on research design [lovingly known to all exposed as KKV] I think they regard unit homogeneity and conditional independence as alternative assumptions for causal inference. For example: “we provide an overview here of what is required in terms of the two possible assumptions that enable us to get around the fundamental problem [of causal inference]” (p.91, emphasis mine). However, I don’t see how unit homogeneity on its own can rule out endogeneity (establish the direction of causality). In my understanding, endogeneity is automatically ruled out with conditional independence, but not with unit homogeneity (“Two units are homogeneous when the expected values of the dependent variables from each unit are the same when our explanatory variables takes on a particular value” [p.91]).

Going back to Holland’s seminal article which provides the basis of KKV’s approach, we can confirm that unit homogeneity is listed as a sufficient condition for inference (p.948). But Holland divides variables into pre-exposure and post-exposure before he even gets to discuss any of the additional assumptions, so reverse causality is ruled out altogether. Hence, in Holland’s context unit homogeneity can indeed be regarded as sufficient, but in my opinion in KKV’s context unit homogeneity needs to be coupled with some condition (temporal precedence for example) to ascertain the causal direction when making inferences from data.

The point is minor but can create confusion when presenting unit homogeneity and conditional independence side by side as alternative assumptions for inference.

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Dimiter Toshkov

Associate Professor of Public Administration at Leiden University in The Netherlands